Workload-dependent dynamic priority for the multiclass queue with reneging

RAMI ATAR, Anat Lev-Aria

Research output: Contribution to journalArticlepeer-review


Scheduling control for a single-server queue with I customer classes and reneging is considered, with linear holding or reneging cost. An asymptotically optimal (AO) policy in heavy traffic is identified where classes are prioritized according to a workload-dependent dynamic index rule. Denote by ci, µi, and θi, i ∈ : {1, . . ., I} the queue length cost, service rate, and reneging rate, for class-i customers. Then, a relabeling of the classes and a partition 0 w0 < w1 < · · · < wK ∞, K ≤ I are identified such that the policy acts to always assign least priority to the class i when the rescaled workload is in the interval [wi−1, wi). The relabeling is such that when workload is withing the lowest [resp., highest] interval [wi−1, wi), the least priority class is the one with smallest cµ [resp., greatest θ] value. This result stands in sharp contrast to known fluid-scale results where it is AO to prioritize by the fixed cµ/θ index. One of the technical challenges is the discontinuity of the limiting queue length process under optimality. Discontinuities occur whenever the workload reaches one of the levels wi.

Original languageEnglish
Pages (from-to)494-515
Number of pages22
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2018


  • Bellman equation
  • Diffusion control problem
  • Dynamic priorities
  • Multiclass single-server queue
  • Queues with abandonment
  • State-space collapse

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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